Boundedness, global stability, and periodicity of some difference equations
We investigate the boundedness, persistence, and global behavior of solutions of the perennial grass model xn+1=axn+bxn-1e-x n,n=0,1,&ldots;, where a∈0,1, b∈0,∞ , and with positive initial conditions x−1 and x0. ^ We also investigate the boundedness, the global stability, and the periodicity of solutions of the nonlinear second order rational difference equations xn+1=axn+bx n-1A+xn,n =0,1,&ldots; and xn+1=axn+bx n-1A+xn-1, n=0,1,&ldots; where the parameters a,b , and A and the initial conditions x −1 and x0 are nonnegative real numbers. ^
Norman Ray Prokup,
"Boundedness, global stability, and periodicity of some difference equations"
Dissertations and Master's Theses (Campus Access).